It is customary at minchah (the afternoon prayers) on the thirteenth of Adar to give three halves of the coins which serve as the local currency. This money is given to the poor, to do with it as they wish. This contribution is made in memory of the half shekel given by Israel when the Beit haMikdash still stood, and whose forthcoming collection was announced on Rosh Chodesh Adar.
This commemorative act is performed before the reading of the Megillah, since all Israel gathers in the synagogues to hear the Megillah reading. The donation should be given before minchah, for the diligent perform mitzvos as early as possible. Those who reside in cities which were not enclosed by walls [at the time of the conquest of the Land of Israel by Yehoshua] give their money before the Megillah reading on the evening of the fourteenth of Adar. Those who live in Jerusalem [which was enclosed by walls then] give the half shekel donation before the reading of the Megillah on the evening of the fifteenth of Adar.
In a country where there is no coin which is referred to as being half of the local currency, it is customary for the synagogue officials to provide three halves of coins issued elsewhere. These coins are acquired by the members of the congregation who use them to fulfill the custom of giving the half shekel, and are then reacquired by the gabba'im so that others might use them as well. Those who seek to fulfill this requirement in the optimal fashion give the donation for each member of their family, including minors. If their wives are pregnant, they give it for the unborn child as well. Once a father has accepted the custom of giving a donation for each child, he should continue to do so every year.
The reason for the custom of giving three half-shekels is that the Hebrew word terumah donation and the words "half a shekel" are mentioned three times in the Torah portion of Ki Tisa, where the mitzvah of the half shekel is recorded.
The accepted practice is not to view the donation of the half-shekel as releasing one from the mitzvah of giving money to the poor, which is specifically prescribed for Purim.